# CLEAN WORKSPACE AND LOAD PACKAGES --------------------------------------------
rm(list = ls())
library(datasim)
library(tidyverse)
# SIMULATE MULTIVARIATE SPATIAL DATA -------------------------------------------
set.seed(3)
Corr <- matrix(c(1, -0.3, 0, -0.3, 1, 0.3, 0, 0.3, 1), nrow = 3)
sigmas <- rep(0.3, 3)
D <- diag(sigmas)
Cov <- D %*% Corr %*% D
# beta <- c(-0.5, 0, 0.5)
beta <- c(0, 0, 0)
variance <- 0.3 * matrix(c(1, 0, 0, 0, 1, 0, 0, 0, 1), nrow = 3)
cor.model <- "exp_cor"
cor.params <- list(list(phi = 0.04), list(phi = 0.04), list(phi = 0.1))
f <- list(
mean ~ mfe(x1, beta = get("beta")) +
mre(factor(id), sigma = get("Cov")) +
mgp(list(s1), variance = get("variance"), cor.model = get("cor.model"),
cor.params = get("cor.params")),
sd ~ I(0)
)
n <- 300
m <- 3
(data_geo <- sim_model(formula = f, n = n, responses = m))
## # A tibble: 900 x 9
## id x1 s1 mre.factor.mean mgp.list.mean mean sd
## <int> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 -1.29 0.168 0.00419 -0.0457 -0.0415 0
## 2 2 2.64 0.808 -0.490 0.336 -0.154 0
## 3 3 0.487 0.385 0.147 -0.549 -0.402 0
## 4 4 0.854 0.328 -0.306 -0.0600 -0.366 0
## 5 5 1.09 0.602 0.327 -0.228 0.0994 0
## 6 6 0.226 0.604 -0.342 -0.291 -0.633 0
## 7 7 0.0682 0.125 -0.00472 0.433 0.429 0
## 8 8 -0.985 0.295 0.0892 -0.845 -0.756 0
## 9 9 -1.31 0.578 0.960 -0.0223 0.938 0
## 10 10 2.46 0.631 0.0268 0.817 0.843 0
## # ... with 890 more rows, and 2 more variables: response <dbl>,
## # response_label <int>
# knitr::kable(head(data_model, 10))
# VISUALIZE MULTIVARIATE SPATIAL DATA ------------------------------------------
ggplot(data_geo, aes(x1, response)) +
geom_smooth(aes(col = factor(response_label))) +
geom_point(aes(col = factor(response_label)))
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
ggplot(data_geo, aes(s1, mgp.list.mean)) +
geom_line(aes(col = factor(response_label)))
data_geo %>%
dplyr::select(id, mre.factor.mean, response_label) %>%
spread(response_label, mre.factor.mean) %>%
dplyr::select(-id) %>%
GGally::ggpairs(aes(fill = "any"))
data_geo_wide <- data_geo %>%
dplyr::rename(ability = response, id_person = id) %>%
gather(var, value, mre.factor.mean:ability) %>%
mutate(var = paste0(var, response_label)) %>%
select(-response_label) %>%
spread(var, value)
# SIMULATE ITEM FACTOR DATA ----------------------------------------------------
q <- 10
init_data <- purrr::map(1:q, ~ data_geo_wide) %>%
purrr::reduce(rbind)
# n <- 300
difficulty <- matrix((1:q - 5)/10 * 2, nrow = 1)
discrimination1 <- seq(0.4, 1.5, length.out = q)
discrimination2 <- runif(q, 0, 2)
discrimination3 <- runif(q, 0, 2)
discrimination1[1] <- 1
discrimination2[1:2] <- c(0, 1)
discrimination3[1:3] <- c(0, 0, 1)
# discrimination1 <- discrimination1 * 0.3
# discrimination2 <- discrimination2 * 0.3
cbind(discrimination1, discrimination2, discrimination3)
## discrimination1 discrimination2 discrimination3
## [1,] 1.0000000 0.0000000 0.00000000
## [2,] 0.5222222 1.0000000 0.00000000
## [3,] 0.6444444 1.3146662 1.00000000
## [4,] 0.7666667 0.5407459 1.31471017
## [5,] 0.8888889 1.7505244 0.36458530
## [6,] 1.0111111 0.2192177 0.15044220
## [7,] 1.1333333 1.0466811 0.03345367
## [8,] 1.2555556 1.3502482 0.12519519
## [9,] 1.3777778 0.4543743 0.25297449
## [10,] 1.5000000 1.3584900 0.37496552
f <- list(
prob ~ mfa(ones, beta = get("difficulty")) +
mfe(ability1, beta = get("discrimination1")) +
mfe(ability2, beta = get("discrimination2")),
# + mfe(ability3, beta = get("discrimination3")),
size ~ I(1)
)
data_long <- sim_model(formula = f,
link_inv = list(pnorm, identity),
generator = rbinom,
responses = q,
n = n,
init_data = init_data
)
data_long <- dplyr::rename(data_long, subject = id,
item = response_label, y = response)
# VISUALIZE ITEM FACTOR DATA ---------------------------------------------------
explor <- data_long %>%
group_by(subject) %>%
summarize(endorse = mean(y),
ability1 = unique(ability1),
ability2 = unique(ability2),
# ability3 = unique(ability3),
x1 = unique(x1))
ggplot(explor, aes(ability1, endorse)) + geom_point(alpha = 0.5)
ggplot(explor, aes(ability2, endorse)) + geom_point(alpha = 0.5)
# ggplot(explor, aes(ability3, endorse)) + geom_point(alpha = 0.5)
# ggplot(explor, aes(x1, endorse)) + geom_point(alpha = 0.5)
Rcpp::sourceCpp("../src/mirt-gibss.cpp")
source("../R/ggplot-mcmc.R")
iter <- 10000
system.time(samples <- ifa_gibbs(data_long$y, n, q, iter, 2))
## user system elapsed
## 337.422 119.141 114.447
samples_tib <- as_tibble.spmirt.list(samples, iter/2)
summary(samples_tib)
## # A tibble: 3,630 x 6
## Parameters `2.5%` `10%` `50%` `90%` `97.5%`
## <fct> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 V1 -1.44 -0.953 -0.0924 0.783 1.29
## 2 V2 -0.844 -0.384 0.539 1.47 1.99
## 3 V3 -2.24 -1.68 -0.765 0.125 0.649
## 4 V4 -1.82 -1.34 -0.494 0.375 0.883
## 5 V5 -1.82 -1.33 -0.466 0.404 0.929
## 6 V6 -1.22 -0.805 0.0169 0.917 1.40
## 7 V7 -0.923 -0.369 0.668 1.63 2.14
## 8 V8 -2.76 -2.25 -1.28 -0.334 0.202
## 9 V9 -0.322 0.228 1.34 2.33 2.92
## 10 V10 -0.414 0.0143 0.892 1.84 2.41
## # ... with 3,620 more rows
samples_long <- gather(samples_tib)
as_tibble.spmirt.list(samples, 0, 10, "c") %>%
gg_trace(alpha = 0.6)
as_tibble.spmirt.list(samples, 0, 10, "a") %>%
gg_trace(alpha = 0.6)
as_tibble.spmirt.list(samples, iter/2, 10, "a") %>%
gg_density(alpha = 0.5, ridges = TRUE, aes(fill = Parameters), scale = 4)
## Picking joint bandwidth of 0.0718
as_tibble.spmirt.list(samples, iter/2, 10, "theta") %>%
dplyr::select(1:100) %>%
gg_density(alpha = 0.5, ridges = TRUE, aes(fill = Parameters), scale = 4)
## Picking joint bandwidth of 0.184
as_tibble.spmirt.list(samples, 0, 10, "theta") %>%
select(1:10) %>%
gg_trace(alpha = 0.6)
as_tibble.spmirt.list(samples, 0, 10, "a") %>%
gg_density2d(`Discrimination 1`, `Discrimination 2`, each = 10,
keys = c("Item ", "Discrimination "),
highlight = c(discrimination1, discrimination2))
## Warning: Computation failed in `stat_density2d()`:
## bandwidths must be strictly positive
as_tibble.spmirt.list(samples, 0, 10, "a") %>%
gg_scatter(`Discrimination 1`, `Discrimination 2`, each = 10,
keys = c("Item ", "Discrimination "),
highlight = c(discrimination1, discrimination2))
as_tibble.spmirt.list(samples, iter/ 2, select = "a") %>%
summary() %>%
mutate(param = c(discrimination1, discrimination2)) %>%
gg_errorbarh() +
geom_point(aes(param, Parameters), col = 3)
as_tibble.spmirt.list(samples, iter/2, select = "c") %>%
summary() %>%
mutate(param = as.numeric(difficulty)) %>%
gg_errorbarh() +
geom_point(aes(param, Parameters), col = 3)
as_tibble.spmirt.list(samples, iter/2, select = "theta") %>%
dplyr::select(1:300) %>%
summary() %>%
mutate(param = data_geo$response[1:300]) %>%
gg_errorbarh(sorted = TRUE) +
geom_point(aes(x = param), col = 3)
as_tibble.spmirt.list(samples, iter/2, select = "theta") %>%
dplyr::select(301:600) %>%
summary() %>%
mutate(param = data_geo$response[301:600]) %>%
gg_errorbarh(sorted = TRUE) +
geom_point(aes(x = param), col = 3)
ability1_pred <- as_tibble.spmirt.list(samples, iter/2, select = "theta") %>%
dplyr::select(1:300) %>%
summary() %>%
mutate(param = data_geo$response[1:300],
s1 = data_geo$s1[1:300],
s2 = s1,
estim = `50%`)
ability1_pred %>%
ggplot(aes(s1, `50%`)) +
geom_line() +
geom_line(aes(s1, param, col = "real"))
vg <- gstat::variogram(estim ~ 1, ~ s1 + s2, ability1_pred, cutoff = 1, width = 0.01)
ggplot(vg, aes(dist, gamma)) +
geom_point(aes(size = np)) +
geom_smooth() +
expand_limits(y = 0, x = 0) +
scale_x_continuous(limits = c(0, 0.7))
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
## Warning: Removed 30 rows containing non-finite values (stat_smooth).
## Warning: Removed 30 rows containing missing values (geom_point).
ability2_pred <- as_tibble.spmirt.list(samples, iter/2, select = "theta") %>%
dplyr::select(301:600) %>%
summary() %>%
mutate(param = data_geo$response[301:600],
s1 = data_geo$s1[301:600],
s2 = s1,
estim = `50%`)
ability2_pred %>%
ggplot(aes(s1, `50%`)) +
geom_line() +
geom_line(aes(s1, param, col = "real"))
vg <- gstat::variogram(estim ~ 1, ~ s1 + s2, ability2_pred, cutoff = 1, width = 0.01)
ggplot(vg, aes(dist, gamma)) +
geom_point(aes(size = np)) +
geom_smooth() +
expand_limits(y = 0, x = 0) +
scale_x_continuous(limits = c(0, 0.7))
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
## Warning: Removed 30 rows containing non-finite values (stat_smooth).
## Warning: Removed 30 rows containing missing values (geom_point).
# # PREPARE DATA FOR MODELLING ---------------------------------------------------
#
# Y <- data_model %>% dplyr::select(id, response, response_label) %>%
# spread(response_label, response) %>%
# arrange(id) %>%
# dplyr::select(-id) %>%
# as.matrix()
#
# X <- data_model %>% dplyr::select(id, matches("^x[[:digit:]]+$")) %>%
# unique() %>%
# arrange(id) %>%
# dplyr::select(-id) %>%
# as.matrix()
#
# Beta <- matrix(beta, nrow = 1)
# Sigma_proposal <- diag(1, 3)
#
# # RUN MODEL --------------------------------------------------------------------
#
# getwd()
# Rcpp::sourceCpp("../src/multi-lm.cpp")
# source("../R/ggplot-mcmc.R")
#
# iter <- 10^6
# system.time(
# samples <- multi_lm(Y, X, iter, 0.01 * Sigma_proposal, 0.001 * Sigma_proposal)
# )
# samples %>% map(~ tail(.))
#
# # apply(samples$beta, 2, mean)
# # cor(samples$beta)
#
# # Visualize traces
# as_tibble(samples, 0, 100, select = "beta") %>%
# gg_trace(wrap = TRUE, alpha = 0.6)
#
# as_tibble(samples, 0, 100, select = "beta") %>% gg_trace(alpha = 0.6)
# as_tibble(samples, 0, 100, select = "corr_chol") %>% gg_trace(alpha = 0.6)
# as_tibble(samples, 0, 100, select = "corr") %>% gg_trace(alpha = 0.6)
# as_tibble(samples, 0, 100, select = "sigmas") %>% gg_trace(alpha = 0.6)
#
# bla <- as_tibble(samples, iter/2, select = "sigmas")
# cov(log(bla))
# nrow(unique(bla)) / nrow(bla)
#
# bla <- as_tibble(samples, iter/2, select = "corr_chol")
# cov(bla)
# nrow(unique(bla)) / nrow(bla)
#
# # Visualize densities
#
# as_tibble(samples, iter / 2, select = "corr_chol") %>%
# gg_density(aes(fill = Parameters), scale = 2, alpha = 0.5, ridges = TRUE)
#
# as_tibble(samples, iter / 2, select = "corr") %>%
# gg_density(aes(fill = Parameters), scale = 1, alpha = 0.5, ridges = TRUE)
#
# # Visualize credible intervals
# as_tibble(samples, iter / 2, select = "beta") %>%
# summary() %>%
# mutate(param = beta) %>%
# gg_errorbarh() +
# geom_point(aes(param, Parameters), col = 3)
#
# Corr_chol <- t(chol(Corr))
# corr_chol <- Corr_chol[lower.tri(Corr_chol, diag = TRUE)]
# corr <- Corr[lower.tri(Corr)]
#
# as_tibble(samples, iter / 2, select = "corr_chol") %>%
# summary() %>%
# mutate(param = corr_chol) %>%
# gg_errorbarh() +
# geom_point(aes(param, Parameters), col = 3)
#
# as_tibble(samples, iter / 2, select = "corr") %>%
# summary() %>%
# mutate(param = corr) %>%
# gg_errorbarh() +
# geom_point(aes(param, Parameters), col = 3)
#
#
# as_tibble(samples, iter / 2 ,select = "sigmas") %>%
# summary() %>%
# mutate(param = sigmas) %>%
# gg_errorbarh() +
# geom_point(aes(param, Parameters), col = 3)
#
#
# # Visualize credible intervals for all Parameters
# as_tibble(samples, iter / 2) %>%
# summary() %>%
# mutate(param = c(beta, corr_chol, corr, sigmas)) %>%
# gg_errorbar() +
# geom_point(aes(Parameters, param), col = 3)
#